You may have heard about "Levels of Measurement" assigned to variables in
statistics, specifically Nominal, Ordinal, Interval, and Ratio- level data. And you
have probably also heard other terms used to describe variables, such as
Categorical, Continuous, Qualitative, and Quantitative. I am going to connect all
of these statistical dots for you in this brief review of
levels of measurement.
When we use statistics, we are representing the world with numbers.
Our numbers tend to do one of two things: one, they help us to create categories, or
two, they help us to measure something. Categorical variables come in two
varieties: ordered categories or unordered categories. Your variable may
be an ordered category, such as "class standing" as freshman, sophomore, junior,
senior. Or "income status" as labor, supervisor, management, executive. Or level
of education: Bachelor, Master, Doctorate. Because of the underlying hierarchy - or
order - in the data, these are "Ordinal" data.
But if the categories are just groups, with no underlying order, such as Blue Team,
Red Team, Yellow Team; or male, female; or experimental versus control groups.
Well then a number representing that category is nothing more than a name, and so we
call it "Nominal" data. Categorical variables are also called "Qualitative
variables", because they describe a quality of the variable, like its name or
its group, rather than an amount or a quantity. If the categorical variable can
have only two levels, then it is also called dichotomous. For example, you
can only be in the ALIVE group or you can be in the DEAD group. You cannot be
in both, you cannot be in neither. You are one or the other.
The measurement variables use scales that have equal intervals on the scales.
We distinguish these scales by whether or not they have a meaningful zero point.
If you are measuring height in inches, or weight in pounds, or points earned on a
test, each of these scales has an absolute zero. You can have zero inches,
or zero pounds, or zero points, but you cannot have less than zero. These are
called "Ratio" data. Other scales measure something, and have equal intervals on
the scale, but do not have a meaningful zero. If we measure your IQ score, or a
test of your personality, or we measure temperature on a scale like Fahrenheit
or Celsius, each of these have equal interval scales,
but none of them have a meaningful zero point. Either you cannot actually score a
zero - such as with an IQ test - or you could score less than zero - such as 20
degrees below zero Fahrenheit. These are called
"Interval" data, because they have equal intervals on the scale, but they do not
have an absolute zero. If your scale can have negative numbers
then it is an interval (not a ratio-level) scale. Measurement variables are also
called "Quantitative", because they describe an amount or a quantity of the
variable, generally telling us "how much" of the variable is present. How much do
you weigh? How much do you agree with this statement? So to review, our
numbers or data can define categories or they can measure something.
Categorical variables can be unordered or ordered. Unordered categories are
nominal, and ordered categories are ordinal. Categorical variables are
qualitative variables, and they are discrete, because they usually have only
whole numbers - no decimals or fractions. All of our measurement scales have equal
intervals, and some kinds have a meaningful zero point. Scales without a
meaningful zero are called interval scales and scales with an absolute zero
are called ratio, but all that really matters for
our purposes is that both interval and ratio are scales. Measurement scales are
quantitative, because they tell us how much of the variable is present, and they
are continuous in that they can have fractions, decimals, be used in
mathematical formulas, and need not be whole numbers. Got it? Good!!
Let's apply that to our variables.